Forced Visitation?? PLEASE HELP!

I looked for some situation just like mine, but didn't find the precise answer. 

My husband and I are separated.  He has an unusual schedule, so there is no regular visitation.  He has recently begun trying to take the kids (he has a son (10) from a prior relationship) on Tuesdays.  Our daughter (7) has some trouble with her relationship with him.  I'm not sure if it's because I was a stay at home mom with her and he worked a lot, or what, but she is extremely attached to me.  She has expressed not wanting to go, even when her brother is there.

Today was the mother of all tantrums.  She knew he was coming and expressed her desire not to go.  I told her that he's her dad, and that he had a fun evening planned.  I said that her brother was going.  He said he would be taking her Monday, and I told her Monday.  The tantrum was BAD. 

I was torn between not giving into the tantrum and forcing her to go (don't reward bad behavior), and forcing her to go.  You hate to force a kid, who feels good about that?  We attempted that, thinking it was in hers and her dad's best interest, but the kicking and screaming was insane.  He tried to buckle her in the car but she wouldn't stay still enough to get buckled in and have the door closed.  He asked me what I told her to cause her to behave that way.  I always tell her that even if daddy and I don't end up together it's important for her to have a good relationship with him.  Tonight was supposed to be fun.  They were going to have a campfire, roast marshmallows, and make mountain pies.

I read the example where the ex grinned when the child wouldn't go with daddy.  I ENCOURAGE her to go.  I am most certainly NOT against it.  That particular example stated to calmly tell them they have to go and firmly insist that the child goes.  We tried that.  There was no firmly insisting she go.  Neighbors opened their doors and stared.  Both of us were upset, raising our voices, and crying.  I have a migraine, so I really wanted the evening to rest.

SO - What do you do when the child doesn't want to go and throws a tantrum so strong you can't force them into the car.  I was scared she would unbuckle herself and be unsafe even if he engaged the child locks.  We tried all the logical choices - Be calm.  Encourage.  Tell her how fun it would be. 

I do NOT want her manipulating the situation, but I don't want her to have to basically be put in a straight jacket in order to go.  I did tell her no TV and go to bed early tonight.  NOT because so much of not going with her dad, but because the temper tantrum behavior was not acceptable.

This is not a case of one spouse wanting it and the other not, or a case of a parent being mean, or turning a child against a parents.  Two parents that want the best for their child, and a child resisting - intensely.  Help is welcome, especially if someone might be a counselor or therapist!